Lesson 1.3.1: Intro to transformations |
For this lesson there are 9 steps for you to take. Scroll down and do each step one-by-one. The instructions under each step will help clarify exactly what you need to do, so please read all the instructions.
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Here is your Lesson 1.3.1 Worksheet
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Whole Class Warm Up
We will do a couple problems as a class for each activity below. Then it will be your turn to complete the following Khan Academy Activities.
Make sure to sign in to Khan when you get there.
We will do a couple problems as a class for each activity below. Then it will be your turn to complete the following Khan Academy Activities.
Make sure to sign in to Khan when you get there.
- Translations: https://www.khanacademy.org/math/geometry/transformations/rigid-transformations-intro/e/performing-translations-on-the-coordinate-plane
- Rotations: https://www.khanacademy.org/math/geometry/transformations/rigid-transformations-intro/e/performing-rotations-on-the-coordinate-plane
- Reflections: https://www.khanacademy.org/math/geometry/transformations/rigid-transformations-intro/e/performing-reflections-on-the-coordinate-plane
1.) Start your notes
Start a new page of notes for Lesson 1.3.1. Title it and write down the targets below:
Targets:
Start a new page of notes for Lesson 1.3.1. Title it and write down the targets below:
Targets:
- I can define the basic transformations.
- I can explain the relationship between functions and transformations.
3.) Important Vocabulary
Explaining how to transform figures without the benefit of a coordinate plane can be difficult without some important vocabulary. Let’s review.
Please write a definition for each of the underlined words.
The word transformation has a specific meaning in geometry. A transformation of the plane is a function that assigns to each point of the plane a unique point in the plane. Transformations that preserve lengths of segments and measures of angles are called basic rigid motions, which include a rotation, reflection, or translation of the plane. Distance Preserving is when the distance between the images of two points is always equal to the distance between the pre-images of the two points. Given a basic transformation, the image of a point A is the point the transformation maps A to in the plane. A dilation is an example of a transformation that preserves angle measures but not the lengths of segments. Angle Preserving is when the angle of any image is equal in measure to that of the pre-image. In other words, a dilation grows or shrinks the pre-image. In this lesson, we will work only with rigid transformations (or rigid motions). We call a figure that is about to undergo a transformation the pre-image while the figure that has undergone the transformation is called the image.
Explaining how to transform figures without the benefit of a coordinate plane can be difficult without some important vocabulary. Let’s review.
Please write a definition for each of the underlined words.
The word transformation has a specific meaning in geometry. A transformation of the plane is a function that assigns to each point of the plane a unique point in the plane. Transformations that preserve lengths of segments and measures of angles are called basic rigid motions, which include a rotation, reflection, or translation of the plane. Distance Preserving is when the distance between the images of two points is always equal to the distance between the pre-images of the two points. Given a basic transformation, the image of a point A is the point the transformation maps A to in the plane. A dilation is an example of a transformation that preserves angle measures but not the lengths of segments. Angle Preserving is when the angle of any image is equal in measure to that of the pre-image. In other words, a dilation grows or shrinks the pre-image. In this lesson, we will work only with rigid transformations (or rigid motions). We call a figure that is about to undergo a transformation the pre-image while the figure that has undergone the transformation is called the image.
4.) Introducing the Transformations Activity
In these next two videos I introduce this activity. Please watch both videos. There are no notes to take, but please give your full attention. |
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5.) Transformations Activity: Your Turn
Now it is your turn. You will need a copy of the images to the right, so please ask me for a copy. Then try to copy the transformation that is taking place. At the same time, compile a list of what steps you need to take to accomplish the transformation. You do NOT need to be perfect on these. This is an exploration activity. You goal is to try to see if you can figure out some steps that are necessary for transformations. The videos to come in the next couple lessons will give you precise steps for these transformations. For now, you are just exploring. |
6.) Look at this website
Click here to go to a website that explains a bit more about transformations. You might like their definitions better than the ones above.
Click here to go to a website that explains a bit more about transformations. You might like their definitions better than the ones above.
7.) Video: Specific Information for Rigid Motions
Earlier in this lesson you were asked to compile a list of the exact information you would need to give somebody if you wanted them to perform a rigid motion transformation (rotation, reflection, translation). If you were like me, it was difficult to know exactly what information would be required to guide somebody to the correct transformation. This video will explain exactly what information is necessary for each type of rigid motion. Please copy the notes that I revealed in the video. |
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8.) Geometry Assumptions
We have now done some work with all three basic types of rigid motions (rotations, reflections, and translations). At this point, we need to state our assumptions as to the properties of basic rigid motions. Please keep these assumptions in mind, and write them in your notes.
We have now done some work with all three basic types of rigid motions (rotations, reflections, and translations). At this point, we need to state our assumptions as to the properties of basic rigid motions. Please keep these assumptions in mind, and write them in your notes.
- Any basic rigid motion preserves lines, rays, and segments. That is, for a basic rigid motion of the plane, the image of a line is a line, the image of a ray is a ray, and the image of a segment is a segment.
- Any basic rigid motion preserves lengths of segments and angle measures of angles.
9.) Exit Ticket
How are transformations and functions related? Provide a specific example to support your reasoning.
After you have written down your answer and example, please show me your work. A high five is on its way.
How are transformations and functions related? Provide a specific example to support your reasoning.
After you have written down your answer and example, please show me your work. A high five is on its way.